Elastic deformations in a perfect bulk Si crystal studied by high-energy X-rays

Long-range strain fields induced in highly perfect bulk crystals during the manufacturing process significantly affect the quality and may even lead to spontaneous fracturing. Obviously a quantitative assessment of these deformations is crucial. A possible means is to examine the diffraction of X-rays by strained crystals, as the deformations bear on the diffraction characteristics of such crystals. In this report a quantitative examination of the diffraction characteristics of a perfect silicon bulk crystal with long-range strain fields in a well defined geometry is presented. The experiments were carried out using a high-energy X-ray laboratory source. By simulating the elastic deformation of the crystal by a finite element program the strain fields of the diffracting crystal are accessed. From these, simulated data values for integrated intensities can be derived on the basis of the dynamical diffraction theory for slightly distorted crystals. The theoretical calculations show good agreement with the experimental measured values. The smallest deformation yielding a noticeable change of the integrated intensity can be associated with a bending radius of the diffracting lattice planes of 16 km.